Block #174,464

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 9/21/2013, 4:26:25 PM · Difficulty 9.8615 · 6,640,588 confirmations

TWN

Bi-Twin Chain

Interleaved pairs of primes that differ by 2, forming twin prime pairs at each level.

Block Header

Block Hash

6c91bf2b361775af6e682aac264f841395564fbb7fa1714d352d4d9eadbd8f91

View on Chainz ↗

Height

#174,464

Difficulty

9.861492

Transactions

Size

7.11 KB

Version

Bits

09dc8ab6

Nonce

552,987

Timestamp

9/21/2013, 4:26:25 PM

Confirmations

6,640,588

Mined by

⛏️ P2SHAX2k1n455i3VkGtcfho7S3iFEiMXfNhABh

Merkle Root

303f925ed9c698f09c3a0ddb31aecd64b78566d497d5adbf640c92d5e98833c3

Transactions (3)

Coinbase365e99062cab54…3d5701c044391f

1 in → 1 out10.3500 XPM109 B

AX2k1n45…MXfNhABh

30f283449491a5…b5775d3979e0b3

58 in → 1 out575.3313 XPM6.55 KB

AL48EMca…MMV6JRSc

71a005207924ba…3984fd50a10c48

2 in → 2 out6.0114 XPM373 B

ATEKeSUq…EJvt2Rey AHYA72s5…EfxHXHjF

Prime Chain Origin

This is the prime chain origin stored in the block header. It is a composite number (not prime itself) — it equals the first prime in the chain multiplied by a primorial. The origin anchors the entire chain to this specific block.

7.842 × 10⁸⁹(90-digit number)

78428682919561156063…12853420021508358399

Discovered Prime Numbers

Lower: 2^k × origin − 1 | Upper: 2^k × origin + 1

These are the actual prime numbers discovered by this block, computed using the verified Primecoin formula. Each number has been independently confirmed to pass the Fermat primality test. Use the FactorDB links to verify any number independently.

Level 0 — Twin Prime Pair (origin ± 1)

origin − 1

7.842 × 10⁸⁹(90-digit number)

78428682919561156063…12853420021508358399

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

7.842 × 10⁸⁹(90-digit number)

78428682919561156063…12853420021508358401

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: origin + 1 − origin − 1 = 2 (twin primes ✓)

Level 1 — Twin Prime Pair (2^1 × origin ± 1)

2^1 × origin − 1

1.568 × 10⁹⁰(91-digit number)

15685736583912231212…25706840043016716799

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.568 × 10⁹⁰(91-digit number)

15685736583912231212…25706840043016716801

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^1 × origin + 1 − 2^1 × origin − 1 = 2 (twin primes ✓)

Level 2 — Twin Prime Pair (2^2 × origin ± 1)

2^2 × origin − 1

3.137 × 10⁹⁰(91-digit number)

31371473167824462425…51413680086033433599

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

3.137 × 10⁹⁰(91-digit number)

31371473167824462425…51413680086033433601

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^2 × origin + 1 − 2^2 × origin − 1 = 2 (twin primes ✓)

Level 3 — Twin Prime Pair (2^3 × origin ± 1)

2^3 × origin − 1

6.274 × 10⁹⁰(91-digit number)

62742946335648924850…02827360172066867199

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

6.274 × 10⁹⁰(91-digit number)

62742946335648924850…02827360172066867201

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^3 × origin + 1 − 2^3 × origin − 1 = 2 (twin primes ✓)

Level 4 — Twin Prime Pair (2^4 × origin ± 1)

2^4 × origin − 1

1.254 × 10⁹¹(92-digit number)

12548589267129784970…05654720344133734399

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 9 consecutive prime numbers forming a Bi-Twin Chain. The prime chain origin — the large number shown above — anchors the chain and is divisible by a primorial (the product of small primes), cryptographically tying these prime numbers to this specific block.

★☆☆☆☆

Rarity

CommonChain length 9

Found in most blocks. The baseline for Primecoin's proof-of-work.

How Primecoin's Proof-of-Work Constructs These Primes

Primecoin stores a value called the prime chain origin in each block. The miner found a large integer such that when divided by a primorial (the product of small primes: 2 × 3 × 5 × 7 × …), the result is the first prime in the chain. The origin is deliberately divisible by this primorial — that divisibility is part of the proof.

Prime Chain Origin = First Prime × Primorial (2·3·5·7·11·…)

Source: Primecoin prime.cpp — CheckPrimeProofOfWork()

This is why the origin has many small prime factors — those factors are the primorial divisor. The chain then extends from the first prime using the TWN formula:

TWN: twin pairs (p, p+2) where p = origin/primorial − 1 and p+2 = origin/primorial + 1

Cross-reference on Chainz Explorer

Block #174,464

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